Square roots of perfect squares — Vedic maths trick
For perfect squares up to 4 digits you can find the square root by looking at the last digit and the first part — no long division.
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The trick
Vilokanam — “by observation”
Last digit → the root ends in one of two digits: 1↔9, 4↔2/8, 9↔3/7, 6↔4/6, 5→5, 0→0.
Remove the last two digits; the biggest square not more than what is left gives the tens digit.
Pick the ending: compare the number with (tens × 10 + 5)² — bigger means the bigger ending.
Use it for: Perfect squares up to 4 digits (roots 11–99).
Worked example: √5184 = 72
Ends in 4 → the root ends in 2 or 8.
Remove 84 → 51; 7² = 49 is the biggest square in 51 → tens digit 7.
75² = 5625; 5184 is smaller → ending 2.
Answer: 72.
Check: 72 × 72 = 5184 ✓
✏️ Practice
Work it out in your head or on paper, type the answer and press Check. Stuck? Press “Show me how”.
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🏁 Trick 9 test
20 sums. Check each answer, then go to the next one. Get 16 or more right to pass.
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